For this question, Imagine a number line with 3 tick marks. The 3 tick marks represent the values x, square root of x, and 3x.
The question asks: “On the number line above, the tick marks are equally spaced. What is the value of x?”
The point midway between x and 3x is 2x. So 2x = sqrt(x) . From there, you can do algebra or just think: what number has a square root that is double the original number? Either way, you land on x = 1/4.
I hope you are not taking tomorrows. If you are just go to sleep please.
Anyways, since we know they are equally spaced, we know that the distance between the first(x) and second (sqrt(x)) one and the distance between the second (sqrt(x)) and third (3x) ones.
The distance between the first and second one is just second ,minus the first
sqrt(x)-x
the distance between the second and third one is just the third minus the second
3x-sqrt(x)t Good fight
So now that we know that these distances are equal, we can set them equal to each other.
sqrt(x)-x=3x-sqrt(x)
all we have to do now is shift stuff over to make it simpler to solve.
2sqrt(x) = 4x
sqrt(x)=2x
x = 4x^2
1 = 4x
x = 1/4
now that we have figured out the answer lets check it to make sure we didn’t screw up
we have 1/4 1/2 3/4
they look evenly spaced (1/4) so this is probably out answer
answer = 1/4
Side note: If you’ve got a nspire cas of any sort, you can use the solve button to save a bunch of time and not have to worry about making careless errors
@NotBadNotGood - your solution is not bad, but not as good as pckeller’s. 
Setting the distances between the midpoint and the outer points equal to each other is the same as equating the middle number to the average of the margins. In case of the margins x and 3x, 2x, obviously, will be smack in the middle.
So, 2x=sqrt(x). Now you can either reason the smart pckeller’s way or divide both sides by sqrt(x):
2sqrt(x)=1
sqrt(x)=1/2
x=1/4.
Or - square both sides, etc., depending on preferences.
Thanks @gcf101 … But I do agree with the first part of @NotBadNotGood 's advice: get some sleep! Most of my students walk around in a state of chronic sleep deprivation. Makes you sad and lowers your scores!
Yup pckeller’s solution is definitely simpler and was posted earlier. Wonder if I just didn’t refresh enough. My bad.